This short study reformulates the statistical Bayesian learning problem using a quantum mechanics framework. Density operators representing ensembles of pure states of sample wave functions are used in place probability densities. We show that such representation allows to formulate the statistical Bayesian learning problem in different coordinate systems on the sample space. We further show that such representation allows to learn projections of density operators using a kernel trick. In particular, the study highlights that decomposing wave functions rather than probability densities, as it is done in kernel embedding, allows to preserve the nature of probability operators. Results are illustrated with a simple example using discrete orthogonal wavelet transform of density operators.
翻译:这个简短的研究用量子力学框架重新表述了贝叶西亚州的统计学习问题。 代表抽样波函数纯状态集合的密度操作员被用在了概率密度上。 我们表明,这种表示方式允许在抽样空间的不同协调系统中提出贝叶西亚州的统计学习问题。 我们还进一步表明,这种表示方式能够利用内核的把戏来了解密度操作员的预测。 特别是,这项研究强调,波函数分解而不是概率密度,正如内核嵌入时所做的那样,允许保留概率操作员的性质。 其结果用一个简单的例子来说明,即使用密度操作员的离心或直方波变换。